PROBLEM III. To find the side of a cubical box that shall contain a quantity equal to any given solidity. RULE. (1) The cube root of the given solidity is the side of a box that will contain the same quantity. Question.-1. How do you find the side of a cubical box that shall contain a quantity equal to any given solidity? EXAMPLES. 1. There is a cylindrical cistern that contains 3204 solid inches; I demand the side of a cubical box, that shall contain the same quantity. 3 3204-14-74+ in. Ans. 2. The side of a cubical cistern, that shall hold just as much liquor as a cask whose solid content is 25519.1196 inches, is required. 25519-1196-29-44† in. Ans. REDUCTION OF COINS. The former currency of New-Hampshire, Vermont, Massachusetts, Connecticut, and Rhode-Island, reduced to dollars, cents, &c. When the sum to be reduced is pounds only. RULE. (1) Annex a cypher to the pounds, divide by 3, the quotient is dollars; if there is a remainder, annex three cyphers, continue dividing, the quotient will be dimes, cents, and mills; 6 shillings is equal to £1×10÷3=3·333. Question.-1. How do you reduce the former currency of the NewEngland States to dollars, cents, and mills, when the sum is pounds? EXAMPLES. 1. It is required to reduce 621 pounds, into dollars, &c. 6210-3 $2070 Ans. and mills. 2. It is required to reduce £19 into dollars, dimes, cents £190 000-3-$63.333† Ans. 3. It is required to reduce £121 to dollars, dimes, cents, Ans. $403.333t. &c. 4. It is required to reduce £16 to dollars, dimes, cents, &c. Ans. $53.333t. When the sum to be reduced consists of pounds, shillings, pence and farthings. RULE.-(1) To the pounds annex half the number of shillings, and two cyphers in decimals, if the shillings are even; if they are odd, annex the greatest even half, and 5 tenths and one cypher in decimals, and divide by 3, the quotient is cents; if there are pence and farthings in the sum, (2) reduce the pence to farthings, observing to increase the sum by 1 if it exceed 12, and by 2 if it exceed 37; add the farthings, thus increased, in the place of tenths and hundredths, divide the whole by 3, the quotient is cents. Questions.-1. If there are shillings in the given sum, what is the method of operation?-2. If there are pence and farthings in the sum, how do you proceed? EXAMPLES. 1. Reduce £3 10s. 114d. to dollars, cents, and mills. 35.00 •48=114d. 35.48 3 $11.826† Ans. 2. Reduce £17 19s. 11ąd. to dollars, cents, and mills. 179.50 179.99÷3=$59.999† Ans. To change dollars, cents, &c. to the former currency of New-Hampshire, Vermont, Massachusetts, Rhode-Island, and Connecticut. RULE.-When the sum to be reduced is dollars; (1) multiply the dollars by 3, double the right hand figure of the product for shillings, the remaining figures are pounds. If the sum to be reduced is dollars, cents, and mills, (2) multiply the whole by 3, point off 4 figures from the right for decimals; the rest of the product is pounds; (note, if mills are not named in the sum, three figures only must be pointed off;) find the value of the decimal part (3) by multiplying by 20, 12 and 4; observing () to point off for decimals each time of multiplying; and the sums standing on the left of the separatrix will be (5) shillings, pence and farthings. Questions.-1. When the sum is dollars, how do you change it into the former currency?-2. If the sum to be reduced is dollars, cents, and mills, what is the method?-3. How is the value of the decimal found?-4. What is to be observed?-5. What will those sums onthe left of the separatrix be? EXAMPLES. 1. It is required to reduce $251 to lawful money. 251X3=£75 6s. Ans. 2. It is required to reduce $9529 to lawful money. 9529X3=£2858 14s. Ans 3. It is required to reduce $192 to lawful money. 192×8 £57 12s. Ans. 4. It is required to reduce $999 to lawful money. £299 14s. Ans. 5. It is required to reduce $99.67 cts. to lawful money. 99.67 29.901 20 18.020 12 240 £29. 18s. 0,24 Ans. 6. It is required to reduce $67.90 to lawful money. Ans. 201. 7s. 41d. 7. It is required to reduce $99.999 to lawful money. Ans. 291. 19s. 11td. 8. It is required to reduce $61.276 to lawful money. Ans. 181. 7s. 7 td. To reduce the former currency of New-York and North Carolina to dols. cts. &c. and the contrary. RULE.-(1) Prepare the sum to be reduced exactly as in New-Hampshire, Massachusetts, &c. and divide by 4 instead of 3, the quotient is cents; a dollar in New-York is equal to (2) 8s. 2 £1×10÷4=$2·50. Questions.-1. What is the method of reducing the former currency of New-York and North-Carolina to dols. cts. &c.?-2. What is a dollar in New-York equal to? EXAMPLES. 1. Reduce £9 16s. to dollars, and cents, &c. 98÷÷4 $24.50 Ans. 2 Reduce £230 10s. to dollars, and cents, &c. 2305-4 $576.25 Ans. 3. Reduce £219 15s. 44d. to dollars, cents, &c. 2197.50 2197 68-4 $549.42 Ans. 4 A merchant in Boston purchased 1200 barrels of flour in New York at £2 10s. per barrel; paid freight at 33 cts. per barrel; what does it stand him at? Ans. $7896. 5. Reduce £419 10s. to dollars, cents, &c. $1048.75 Ans. Change dollars, &c. to New-York and North-Carolina currency. RULE. (1) Proceed as in New-Hampshire currency, &c. only multiply by 4 instead of 3; the value of a dollar is equal to four tenths of a pound. Question.-1. How do you change dollars &c. to New-York and NorthCarolina Currency? EXAMPLES. 1. Change 842 dols. to New-York currency, &c. 842 £336 16s. Ans. 2. Change $114.25 to North-Carolina currency, &c. Ans. £45 14s. New-Jersey, Delaware, Pennsylvania, and Maryland currencies reduced to the present currency of the United States, and the contrary. RULE. (1) Multiply the given sum (if it is pounds only,) by 8, and divide the product by 3; the quotient is dollars. If the sum is pounds, shillings and pence, (2) reduce the whole to pence, and add one ninth of the whole to itself, the sum will be cents; a dollar in these States is equal to (3) 7s. 6d., or of a pound. 7s. 6d. 90d. 24%. £1×8÷3= $2.666. 90 Questions.-1. How do you reduce New-Jersey, Delaware, Pennsylvania, and Maryland currencies to the present currency of the United-States when the sum is pounds only?-2. What is the method of reduction when the sum is pounds, shillings, and pence?-3. What is a dollar in these States equal to? EXAMPLES. 1. It is required to reduce £942 to dollars, &c. 942 3)7536 $2512 Ans. 2. It is required to reduce £961 19s. 10d. to dollars, &c. Ans. $2565.31 cts. Reduce dollars, &c. to the former currency of New-Jersey, Delaware, Pennsylvania, and Maryland. RULE. (1) If the sum is dollars only, multiply by 3, and divide by 8, the quotient is pounds; if the sum is dollars and cents, subtract one tenth of the whole sum from itself, the remainder is pence. Question.-1. What is the rule for reducing dollars, &c. to the former currency of New-Jersey, Delaware, Pennsylvania, and Maryland? EXAMPLES. 1. Reduce 628 dollars to Delaware currency, &c. 628×3-8 £235 10s. Ans. 2. Reduce 2512 dollars to New-Jersey currency. Ans. £942. 3. Reduce $2565-20 to Maryland currency, &c. To)2565-20 256.52 subtract. 12)230868 20)19239 £961 19s. Ans. 4. A merchant of Portsmouth purchased 545 barrels of beef at $12.50 per barrel, and sent it to Philadelphia and sold it there for £5 10s. per barrel; deducted the freight at 30 cts. per barrel, and laid out the remainder of the money in flour, at £3 10s per barrel, and sent it to Portsmouth, |